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Dependently Typed Records in Type Theory
Formal Aspects of Computing, 2002Abstract.The languagePebbleof Burstall and Lampson proposed dependent types as the underlying principle in a unified framework to explain facilities for programming in the large, such asmodulesandsignatures, as well as for programming in the small. This proposal soon extended to large scale formal proof development as well.
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Proceedings and Addresses of the American Philosophical Association, 1973
In this paper I advocate a reexamination of mathematical logic in the tradition of Principia Mathematica and the early writings of Russell ([PoM], [OD], [ML]), to ask in what form it should now be studied in order to preserve certain important contributions of Russell and in order to compare it with the somewhat different Fregean tradition. This should
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In this paper I advocate a reexamination of mathematical logic in the tradition of Principia Mathematica and the early writings of Russell ([PoM], [OD], [ML]), to ask in what form it should now be studied in order to preserve certain important contributions of Russell and in order to compare it with the somewhat different Fregean tradition. This should
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Embedding intuitionistic-type theory in negationless-type theory
Mathematical Notes of the Academy of Sciences of the USSR, 1986In ''A formal system of negationless arithmetic that is consistent with respect to Heyting arithmetic'' [Mat. Zametki 36, No.4, 583-592 (1984; Zbl 0576.03037)] the author shows that Heyting arithmetic is a conservative extension of \(HA^ N\)- a system of negationless arithmetic, under certain interpretation.
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Journal of Symbolic Logic, 1971
In [8] J. A. Robinson introduced a complete refutation procedure called resolution for first order predicate calculus. Resolution is based on ideas in Herbrand's Theorem, and provides a very convenient framework in which to search for a proof of a wff believed to be a theorem. Moreover, it has proved possible to formulate many refinements of resolution
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In [8] J. A. Robinson introduced a complete refutation procedure called resolution for first order predicate calculus. Resolution is based on ideas in Herbrand's Theorem, and provides a very convenient framework in which to search for a proof of a wff believed to be a theorem. Moreover, it has proved possible to formulate many refinements of resolution
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Abstract Data Types and Type Theory: Theories as Types
Mathematical Logic Quarterly, 1991Ruy J. G. B. de Queiroz +1 more
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1994
Introduction D iscussion 3.1.1 The fundamental idea of algebraic type theory is to provide a formal framework for reasoning using the usual rules of equality. Simple algebraic type theory is far removed from the syntax and rules of real programming languages, but it is a good starting point from which to motivate and explain the ideas of ...
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Introduction D iscussion 3.1.1 The fundamental idea of algebraic type theory is to provide a formal framework for reasoning using the usual rules of equality. Simple algebraic type theory is far removed from the syntax and rules of real programming languages, but it is a good starting point from which to motivate and explain the ideas of ...
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A new era of cancer immunotherapy: converting theory to performance
Ca-A Cancer Journal for Clinicians, 1999Steven A Rosenberg
exaly